Detecting non-stationary in the unit hydrograph Barry Croke 1,2, Joseph Guillaume 2, Mun-Ju Shin 1 1 Department of Mathematics 2 Fenner School for Environment and Society

Outline Data analysis methods – detecting variability in the shape of the UH without resorting to a model Adopting a UH model to explore variability in the UH shape between calibration periods Comparison between different models Testing structures of the non-linear module, and attempting to capture the variability in the UH shape

Data analysis methods Direct estimation for Axe Creek 49 peaks accepted in total 13 large peaks (>4cumecs) 28 small peaks (<3cumecs) Croke, A technique for deriving the average event unit hydrograph from streamflow-only data for quick-flow-dominant catchments, Advances in Water Resources. 29, , doi: /j.advwatres

Pareto analysis of cross-validation results Identify one or more models per calibration period, and calculate performance in each calibration period Ignore dominated models - inferior in all periods, retain the rest – no reason to eliminate them Consider the range of non-dominated performance (RNDP) Croke, Exploring changes in catchment response characteristics: Application of a generic filter for estimating the effective rainfall and unit hydrograph from an observed streamflow timeseries, BHS

Apparent non-stationarity in UH Catchmentmax R 2 RNDP Bani Garonne Fernow Flinders Real Wimmera Ferson Catchmentmax R 2 RNDP Allier Kamp-Zwettl Axe creek Lissbro Gilbert Durance Blackberry

Comparison of different models IHACRES-CMD (Croke and Jakeman, 2004), 2 stores model used fixed parameters: e=1 (potential evapotranspiration data used); d=200 calibrated parameters: f=( ); tau_q=(0-10); tau_s=( ); v_s=(0-1) GR4J (Perrin, 2000, 2003), 4 parameters SIMHYD (Chiew et al., 2002), 9 parameter version used (Podger, 2004) Sacramento (Burnash et al., 1973), 13 parameters Calibration algorithm: Shuffled Complex Evolution algorithm

Questions 1.What is the Range of Non-Dominated Performance (RNDP) across all periods? 2.What is the RNDP in each period? Is it low even though total RNDP is high? Why? 3.Which rainfall-runoff model has more Pareto-dominated models? 4.Which non-dominated model has the worst performance in each period? Is it consistently the same dataset (pattern)? Is there reason for that period to be problematic?

Results Range of non-dominated performance (RNDP) is >0.1 for all catchments, but highly variable 3 catchments (Allier, Ferson and Real) have periods that increase the RNDP with R 2 (NSE) RNDP reduced when R 2 log is used GR4J has the most non-dominated cases Worst models are SIMHYD (R 2 ) and Sacremento (R 2 log ) Five catchments (Durance, Ferson, Garonne, Kamp- zwettle and Real) have pattern of problematic behaviour (from the viewpoint of the models)

Exploring structure of non-linear module Performance of stationary UH Modified structure to permit variation based on catchment wetness Compensating for suspected intense events

CMD module formulations Stationary UH Linear Bilinear Sin Exponential Power law Variable UH 2 effective rainfall time series Intense events

Adopted structures Most common: sinusoidal (9 catchments) Mostly low order Nash cascades (2-3 stores) AllierExponential5 Axe CreekBilinear2 BaniSinusoidal4 BlackberryExponential3 DuranceSinusoidal7 FernowBilinear2 FersonBilinear1 FlindersExponential3 GarroneSinusoidal4 GilbertSinusoidal2 Kamp-zwettlSinusoidal3 LissbroSinusoidal3 RealSinusoidal2 WimmeraBilinear4

Apparent non-stationarity in UH Catchmentmax R 2 RNDP Bani Garonne Fernow Flinders Real Wimmera Ferson Catchmentmax R 2 RNDP Allier Kamp-Zwettl Axe creek Lissbro Gilbert Durance Blackberry

Axe Creek: period 1 (1.16)

Allier: period 1 (0.26)

Bani: period 1 (0.04)

Allier: period 1

Axe Creek: correction for variable UH

Axe Creek: period 1

Conclusion A key source of non-stationarity in many catchments is variability in the shape of the UH Seen as a trend in model residual against observed flow – not present in when plotted against modelled flow, so produced by an unknown driver Hypothesis: variability is a result of event-to-event variations in rainfall intensity, and is predominantly a problem when using daily data Need to overcome this before addressing smaller effects

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